Problem 14 · 2014 Math Kangaroo
Hard
Geometry & Measurement
areasubstitution
Five congruent rectangles are positioned inside a square of side length 24, as shown in the diagram. What is the area of one of these rectangles?
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Answer: E — \(32\text{ cm}^2\)
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Hint 1 of 2
Call the rectangle's long side L and short side W, then read off the side of the square along two directions.
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Hint 2 of 2
The staircase forces a relation between L and W; solve it together with the side length 24.
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Approach: set up length equations from the staircase
- Let the rectangle be L by W. Reading across one direction of the staircase and down the other gives equations that link L and W to the square's side 24.
- Solving them yields a long side that is twice the short side, with L = 8 and W = 4.
- So one rectangle has area 8 × 4 = 32 cm².
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